How do I do I unwrap from a point of view?
You can try this:


Select your objects and go to edit mode
Select all faces of the both objects and switch to Top view
From the menu select UV -> Project From View
Switch to object mode and create a material for one of the objects
Add your texture to the material
Make sure you create a Texture Coordinate node and connect the UV slot to the Vector slot of your image texture.
Apply the same material to the other object.




Edit:

This was added to the question:
"I don't want to affect the plane UV map"  

In this case you can use the Data Transfer modifier on your Cube to transfer the UVs form the Plane to the Cube (I used a Torus instead, it's a bit more visible)  


Position the Cube somewhere above the Plane
Use Data Transfer modifier on the Cube
In the modifier settings as the Source select your Plane
Check Face Corner Data with Nearest Face Interpolated settings
Click on UVs
You might need to click Generate Data Layers  


For the Data Transfer modifier to work properly you will need more edges/subdivision on your Plane.
If you don't apply the modifier you can move your Cube and the UV data will adapt to the new position.